Math Problem Statement

ln(x)=2.896

Solution

To solve the equation ln(x)=2.896\ln(x) = 2.896, we can rewrite it in exponential form:

x=e2.896x = e^{2.896}

Now, we calculate e2.896e^{2.896}:

x18.091x \approx 18.091

Thus, the solution is:

x18.091x \approx 18.091

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

  1. How do you solve an equation with a natural logarithm and an additional constant?
  2. What is the general approach for solving logarithmic equations?
  3. How do you graph logarithmic functions?
  4. What are the properties of the natural logarithm ln(x)\ln(x)?
  5. How is the base ee used in real-world applications like growth and decay?

Tip: Remember, ln(x)\ln(x) is the natural logarithm, which means it's the logarithm with base e2.718e \approx 2.718.

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Math Problem Analysis

Mathematical Concepts

Algebra
Logarithmic Functions
Exponential Functions

Formulas

ln(x) = y => x = e^y
e^2.896 ≈ 18.091

Theorems

Properties of Natural Logarithms
Inverse Relationship between Logarithms and Exponentials

Suitable Grade Level

Grades 9-12